The size increase of a nanoscale material is commonly associated with the increased stability of its ordered phases. Here we give a counterexample to this trend by considering the formation of the defect-free L11 ordered phase in AgPt nanoparticles, and showing that it is better stabilized in small nanoparticles (up to 2.5 nm) than in larger ones, in which the ordered phase breaks in multiple domains or is interrupted by faults. The driving force for the L11 phase formation in small nanoparticles is the segregation of a monolayer silver shell (an Ag-skin) which prevents the element with higher surface energy (Pt) from occupying surface sites. With increasing particle size, the Ag-skin causes internal stress in the L11 domains which cannot thus exceed the critical size of ~2.5 nm. A multiscale modelling approach using full-DFT global optimization calculations and atomistic modelling is used to interpret the findings.